The first of these is that rangers are better. While not objectively false, many would say that paratroopers are better, with the key being tactical movement and the extra man. The extra man means both an extra carbine
The next issue is your comparison between the 1919 upgrade and the thompsons. It's almost entirely subjective, so I'll just say that the thompson is definitely the preferred upgrade of the two at the top level. The point I'm trying to make is that people would probably say that 1919 paras are less useful than thompson paras, and I think your suggestions are skewed in an unnecessary direction because of it.
On that, your suggestions give them utility and power in a role that people were not using them in (I'm primarily referencing Dave with all of this by the way). Paras simply have insane raw DPS - roughly 20% more than shocks at point blank, all while having significantly more generous DPS curve and tactical movement. Paras are mainly used for retreat path wipes, they're usually not the unit forcing the retreat. They're the second part of a one-two punch, and I think sprint would turn them into more of a haymaker. This is fine, but I think they operate as they should
within their current niche.
Drawing from the previous point about DPS, I think giving them camo when they have THAT much DPS is indeed a bad idea. Paras actually are a different level than Ostheer storm troopers, and British commandos. As for partisans, paras have about 10 partisan models worth of DPS...
Falls are kind of a unit that don't belong in this category IMO. Their DPS curve can be simplified down to that of a super bolt action rifle. They have that same lacking moving performance too. The thing about most ambush units is that they either:
1. Let the enemy get closer, so that they can get into their (relative to the other squad theyre facing) preferred range and win the engagement. This is what partisans have to do since it's the only way they can win a fight. Their low DPS at all ranges means that they're not going to get a wipe.
2. Let the enemy get closer so that they can maximize their own DPS. This is done regardless of what range your enemy's squad prefers to be, because you just want a wipe. Commandos and storm troopers have high enough maximum DPS to do this.
The thing is that falls fall into neither of these two categories for AI ambush units. They don't want or need their enemies to get close because they have a rifle profile (meaning that close range is usually favorable for the enemy relative to long range), and because they can already win long range fights. They don't have the raw DPS to wipe squads on their ambush either. Also, their effective durability still kind of sucks - it's less than that of volks. Point is, I don't think they should be in the comparison for stealth units.
Edit: Giving this post a conclusion/tl;dr: paras have a niche that they perform fairly well in as-is. I think that any suggestions to change them should keep their current role in mind, and whether or not they should be given the ability to act in another role (either in replacement or addition). Personally, I'm not quite convinced by your suggestions and the reasonings.